一类拟线性抛物型问题的爆破集

张海亮

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一类拟线性抛物型问题的爆破集

应用基础研究 | 更新时间：2026-09-14

- 一类拟线性抛物型问题的爆破集
- Blow-up Set of a Class of Quasilinear Parabolic Problem
- 中北大学学报（自然科学版） 2008年第2期页码：105-108
- 作者机构：
  
  浙江海洋学院数理信息学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(10771128);山西省自然科学基金资助项目(20051004)
- DOI：
  中图分类号：
- 纸质出版：2008
- 稿件说明：
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张海亮. 一类拟线性抛物型问题的爆破集[J]. 中北大学学报（自然科学版）, 2008,(2):105-108.

张海亮. Blow-up Set of a Class of Quasilinear Parabolic Problem[J]. 2008, (2): 105-108.
张海亮. 一类拟线性抛物型问题的爆破集[J]. 中北大学学报（自然科学版）, 2008,(2):105-108. DOI：

张海亮. Blow-up Set of a Class of Quasilinear Parabolic Problem[J]. 2008, (2): 105-108. DOI：

摘要

主要研究了一般拟线性抛物型方程在Dirichlet边界条件下正解的爆破集

是Friedman 1987年结果的重要推进.以反演原理、辅助函数法和经典抛物型方程的极大值原理为工具

证明了问题正解的爆破集是一紧子集

并获得了解的爆破率

即爆破解关于时间t的估计.最后

将结果应用到基于流体力学和生物学背景的两个数学模型.

Abstract

The blow-up set of the positive solutions of a class of quasilinear parabolic equations subject to Dirichlet boundary conditions was studied

which deepened ones from the corresponding work of Friedman in 1987.The result that the blow-up set of the problem is a compact subset was proved by the reflective principle and the maximum principle

and the blow-up rate of the solutions was obtained.As applications of the results

two examples for fluid mechanics and biology were given in the end of the paper.

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references

Friedman A,McLeod J B.Blow-up of positivesolutions of semi-linear heat equations[J].Indiana Math.J,1985,34:425-447.

Friedman A.Partial Differential Equationsof Parabolic Type[M].Prentice-Hall,1967.

Wang L,Chen Q Y.On the blow-up for quasilinear parabolic equations[J].J.Partial Diff.Equations,1993,2:117-120.

Ladyzenskaja O A,Uralceva N N,Solonnikov V A.Linear and Quasilinear Equations of Parabolic Type[M].AMSTranslations of Math.Monographs,1988:23.

Qi Yuanwei.The asymptotics of blow-up solutions adegenerate parabolic equations[J].J.Appl.Math.Phys.(ZAMP),1991,42:488-496.

Hu Bei,Yin Hongming.The profile near blowup timefor solution of the heat equation with a nonlinear boundary-condition[J].Transactions of the American Mathematical Society,1994,346:117-135.

Ding Juntang,Li Shengjia.Blow-up solutions and global solutions for a class ofquasilinear parabolic equations withrobin boundary conditions[J].Comput.Math.Appl,2005,49:689-701.

Zhang Hailiang.Blow-up of positive solutions of quasilinear parabolic equations with mixed boundary conditions[J].Commmunications in Mathematical Analysis,2007,2(1):53-60.

Zhang Hailiang,Liu Zengrong,Zhang Wu.Growth estimates andblow-up in quasilinear parabolic problems[J].Applicable Analysis,2007,86:261-268.

Allen L J.Persistence andextinction in single-species reaction-diffusion models[J].Bull.Math.Biol,1983,45:209-227.

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